Question

Question 8
Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Answer 1

F = 10
E = 20
V = 15
Any polyhedron satisfies Euler’s formula, according to which, F + V – E = 2
For the given polygon, F + V – E = 10 + 15 – 20 = 25 – 20 = 5, which is not equal to 2
Since Euler’s formula is not satisfied, such a polyhedron is not possible.